select a counterexample for the given invalid argument.
-1. (∃x)(∼Ax ≡ Cx)
2) (∃x)(Ax • Cx)
3) (∀x)(Bx ⊃ Ax) / (∀x)(Cx ⊃ Bx)
A) Counterexample in a domain of 2 members, in which: Aa: True Ba: False Ca: True
Ab: True Bb: True Cb: False
B) Counterexample in a domain of 2 members, in which: Aa: False Ba: False Ca: True
Ab: True Bb: True Cb: False
C) Counterexample in a domain of 2 members, in which: Aa: True Ba: True Ca: True
Ab: True Bb: True Cb: False
D) Counterexample in a domain of 2 members, in which: Aa: True Ba: False Ca: True
Ab: False Bb: True Cb: False
E) Counterexample in a domain of 2 members, in which: Aa: True Ba: False Ca: True
Ab: True Bb: False Cb: True

Question

Quizplus · Accepted Answer

In the domain of {a,b}, Aa is true and Ba is false, satisfying (∀x)(Bx ⊃ Ax) but disproving (∀x)(Cx ⊃ Bx) as Cb is false and Bb is true. This counterexample shows the argument is invalid.

Select a Counterexample for the Given Invalid Argument